I worked as a Health Visitor, and was very aware of this problem. I completely agree that you must sort it out. I also say this as an individual - in one branch of my family, problems outside the parents' control meant they were heavily reliant on elderly grandparents for childcare, and it was very unsatisfactory. We did not live nearby - I helped out in the school holidays, but found it difficult dealing with children who had been both ignored and indulged by grandparents who, sadly, could not cope.
I would begin by looking yourself at what nursery / childminder provision is available locally and the cost. Depending on the geography and timing, you could get an idea of how things might work out.
You say that they work shifts. This may well work out for you all. Childcare providers normally need families to sign up for regular hours. Your DGD is also at an age where she will benefit from the company of other children and the extra stimulation of a nursery environment. So it may well work for you to have her outside of 'normal' hours.
You should begin a discussion with your daughter & her partner, keeping your own ideas up your sleeve until it seems sensible propose one of the ideas above.
I have a friend whose midwife daughter works 2 nights a week (equivalent to working half a week). The little one arrives at granny's having had his tea. He has a bath, milk & biscuits and a book, then settles for the night. Granny gets him up, gives him breakfast and gets him ready to take to nursery for the morning. Mum picks him up at 1pm, having had a sleep. So mum pays for 8 hours childcare from half a salary, granny contributes a great deal for relatively small effort.
I'd also add, in the meantime, that it may be worth looking out, and going to things like toddler groups, singing groups at the library, baby swim groups etc. Whilst they take effort to get ready and get to, the entertainment they offer (that you don't have to think about) can be very worthwhile.